prove that the length of tangents drawn from an external point to a circle are equal About the author Arya
Answer: Statement: The tangents drawn from an external point to a circle are equal. Given: PT and QT are two tangents drawn from an external point T to the circle C(O,r). To Prove: PT=TQ Construction: Join OT. Solution: We know that a tangent to a circle is perpendicular to the radius through the point of contact. ∴∠OPT=∠OQT=90 ∘ In △OPT and △OQT, ∠OPT=∠OQT(90 ∘ ) OT=OT (common) OP=OQ (Radius of the circle) ∴△OPT≅△OQT (By RHS criterian) So, PT=QT (By CPCT) Hence, the tangents drawn from an external point to a circle are external point to a circle are equal Reply
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Answer:
Statement: The tangents drawn from an external point to a circle are equal.
Given:
PT and QT are two tangents drawn from an external point T to the circle C(O,r).
To Prove: PT=TQ
Construction:
Join OT.
Solution:
We know that a tangent to a circle is perpendicular to the radius through the point of contact.
∴∠OPT=∠OQT=90
∘
In △OPT and △OQT,
∠OPT=∠OQT(90
∘
)
OT=OT (common)
OP=OQ (Radius of the circle)
∴△OPT≅△OQT (By RHS criterian)
So, PT=QT (By CPCT)
Hence, the tangents drawn from an external point to a circle are external point to a circle are equal